On the site, you can put in your 3DS' serial number and find out if you can get your free games. If you haven't been to the Eshop or been online at all, but you bought a 3DS before the 12th of August, you can still scan in your receipt and upload it to the site as a proof that you are eligible.
At least Nintendo Europe finally got round to doing this. Americans and Japanese were able to confirm their eligibility since before the games were made available to download. This whole thing has been quite a failure for Nintendo in general. The games were impossible to find and some people were unsure if they were eligible, with no easy way to find out.
All this coupled with the rumors of a new generation of 3DS with second analogue pad makes things look really bad for Nintendo. They really need to bounce back from this or things could get even worse for them.